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%I #22 Mar 28 2024 09:01:41
%S 1,0,2,4,2,0,0,6,8,0,0,0,4,0,2,0,0,0,6,0,0,0,2,4,2,0,0,6,8,0,0,0,4,0,
%T 2,0,0,0,6,0,0,0,2,4,2,0,0,6,8,0,0,0,4,0,2,0,0,0,6,0,0,0,2,4,2,0,0,6,
%U 8,0,0,0,4,0,2,0,0,0,6,0,0,0,2,4,2,0,0
%N Final digit of n^n - n.
%C Note: cyclic with a period of 20 for n > 0.
%D R. Euler & J. Sadek, "A number that gives the units of n^n", Journal of Recreational Mathematics 29:3 (1998), pp. 203-204.
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%F a(n) = (n^n-n) mod 10
%p [seq((n^n-n) mod 10, n=1..40)];
%t Join[{1}, Table[Mod[PowerMod[n, n, 10] - n, 10], {n, 100}]] (* _T. D. Noe_, Mar 13 2012 *)
%t PadRight[{1},120,{0,0,2,4,2,0,0,6,8,0,0,0,4,0,2,0,0,0,6,0}] (* _Harvey P. Dale_, May 21 2020 *)
%o (Perl) print (($_**$_-$_)%10) for (1..40);
%o (PARI) a(n)=lift(Mod(n,10)^n-n) \\ _Charles R Greathouse IV_, Mar 13 2012
%Y Cf. A056849.
%K nonn,easy,base
%O 0,3
%A _Radu Borza_, Mar 09 2012
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